Accepted Manuscript

Modelling the properties of liquid foods for use of process flowsheeting simu-
lators: Application to milk concentration

Martial Madoumier, Catherine Azzaro-Pantel, Gaëlle Tanguy, Geneviève

Gésan-Guiziou

PII: S0260-8774(15)00190-9
DOI: http://dx.doi.org/10.1016/j.jfoodeng.2015.04.023
Reference: JFOE 8148

To appear in: Journal of Food Engineering

Received Date: 17 December 2014

Revised Date: 19 March 2015
Accepted Date: 19 April 2015

Please cite this article as: Madoumier, M., Azzaro-Pantel, C., Tanguy, G., Gésan-Guiziou, G., Modelling the
properties of liquid foods for use of process flowsheeting simulators: Application to milk concentration, Journal of
Food Engineering (2015), doi: http://dx.doi.org/10.1016/j.jfoodeng.2015.04.023

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Modelling the properties of liquid foods for use of
process flowsheeting simulators: application to
milk concentration
Martial Madoumier1,2, Catherine Azzaro-Pantel3,*, Gaëlle Tanguy1,2, Geneviève Gésan-Guiziou1,2,*
1
INRA, UMR1253 Science et Technologie du Lait et de l’Œuf, 65 rue de Saint Brieuc, 35000 Rennes,
France
2
AGROCAMPUS OUEST, UMR1253 Science et Technologie du Lait et de l’Œuf, 65 rue de Saint
Brieuc, 35000 Rennes, France
3
Laboratoire de Génie Chimique, UMR5503 CNRS, Université de Toulouse, ENSIACET INPT/UPS, BP
84234, F-31432 Toulouse, France

Keywords
Bovine milk; food product modelling; evaporation; chemical process simulator; food process simulation.

Abstract
In this paper, a modelling approach for liquid food products in a chemical process simulator is proposed
from the flowsheeting methodology widely used for chemical processes. The focus is set on dairy
concentration processes, in which milk is defined as a mixture of water and four dry matter components
(fat, proteins, carbohydrates, minerals) modelled as “pseudo-components” in a conventional simulator
which has been adapted to take into account the behaviour of the liquid food product considered. The
significant properties of milk (heat capacity, boiling point elevation, thermal conductivity, density,
viscosity, surface tension) are modelled with empirical models found in the literature and implemented in
the simulator. In order to validate the approach, an industrial milk evaporation process and a pilot-scale
evaporator are modelled and simulated. The results are compared with industrial and experimental results
respectively, and show a good agreement with the industrial process, however improvements are needed
in modelling the pilot scale evaporator. The proposed approach is generic enough to be extended to other
liquid foods.

Nomenclature
BPE Boiling Point Elevation (°C)
Cp Specific heat (J.g-1.K-1)
DM Dry matter content (mass %)
MW Molecular weight (g.mol-1)
TEMA Tubular Exchanger Manufacturers Association
T Temperature (°C)
TSAT Saturation temperature (°C)
Xi Mass fraction of component “i” (mass/mass)
xSOL Total molar fraction of solutes (mol/mol)
ρ Density (kg.m-3)
λ Thermal conductivity (W.m-1.K-1)
μ Dynamic viscosity (mPa.s)
σ Surface tension (mN.m-1)

1. Introduction
The design and development of sustainable food processes, which integrate technical and economic

*
Corresponding authors. E-mail addresses: genevieve.gesan-guiziou@rennes.inra.fr & catherine.azzaropantel@ensiacet.fr
Tel.: +33 (0)2 23 48 53 25 (G. Gésan-Guiziou) & +33 (0)5 34 32 36 56 (C. Azzaro-Pantel).
1
criteria, satisfy customer demands, and are less harmful to ecosystems, constitute a major challenge in a

context of global changes (climate change, energy scarcity and energy price increase). An interesting way

to meet these constraints entails a systematic approach combining process modelling, simulation, and

process optimisation (Azapagic, Perdan, & Clift, 2011; Lam, Klemes, Kravanja, & Varbanov, 2011).

It is recognized that the chemical and petroleum industries are quite familiar with the simulation-

optimisation approach, and widely use process simulators such as Aspen Plus, Aspen Hysys, ProsimPlus,

Pro/II, and COCO to compute mass and energy balances. These powerful software tools are based on the

modelling of heat and mass transfers inside unit operations and their interconnection, by using

thermodynamic databases. The use of process simulators then requires the exact knowledge of the

composition of the fluids, the specific properties of the individual components and of the involved

mixtures, for which changes in the physico-chemical properties of the product through unit operations are

computed.

Despite the proximity of the chemical and petroleum sectors with the food industry, the development of

this approach in the food sector suffers from two major shortcomings, i.e. a lack of available and

applicable food process models (Trystram, 2012), and a lack of thermodynamic models that account for

the complexity and biological variations of food materials (Carson, 2006; Fito, LeMaguer, Betoret, & Fito,

2007; Lambert, Romdhana, & Courtois, 2013). Thermodynamic models, that allow a complete

understanding of molecular behaviour and a prediction of physical properties of a mixture, are only

known for specific mixtures such as those classically encountered in the chemical industry. They are not

available for food products for which the composition is very complex (more than 2000 molecules in milk

for instance) and their properties depend on both the concentration of their components and the

interaction between them.

Several attempts at modelling liquid food properties have been achieved so that process simulators and

other software tools can be used. Table 1 shows some significant studies which deal with the modelling

and simulation of liquid food processes, with an emphasis on fluid milk. Two main approaches are

proposed (Table 1):

 The food product is defined as a new component (“Unique component approach”, see Table 1).

This approach is the simplest one, since the properties of the food product are specified as constant

2
 or simply depend on temperature, which can be useful to the simulation of the heating or cooling

of food product, or to any process step where there is no change in the composition. This last point

constitutes one of the two major disadvantages of this approach: i) it makes it impossible to

predict changes in physico-chemical properties in the case of a new composition of the feed (e.g.

more fat in the case of milk); ii) it cannot predict the performance of a process versus a change in

properties due to the variation of the composition of the fluid (e.g. concentration) without

modifying the built-in unit operation models of the simulator. Bon et al. (2010) successfully

modelled and optimised a pasteurization process by defining milk as a single component.

Conversely Ribeiro (2001) and Jorge et al. (2010) tried to use this approach to model milk for a

concentration step (where one component (water) is partially removed from the treated product)

but in these cases the development of new unit operation models was necessary to account for

product concentration in the process simulators.

 The food product is divided into several components or “pseudo-components” (“Pseudo-

component approach”, see Table 1), which represent the major categories of chemical components

of the product: water, fat, proteins, carbohydrates, minerals, and fibres. This concept of “pseudo-

components” is already in use in the petroleum industry to model complex mixtures (French-

McCay, 2004), and is similar to the “proximate analysis” of food components (for further details

see Greenfield & Southgate, 2003). In this approach, liquid food is considered as a mixture, the

properties of which being computed by additivity of the properties of the individual “pseudo-

components”. The properties of the individual “pseudo-components” can be modelled in several

ways:

i) by using literature models giving the properties of each individual pseudo-component as a

function of operating parameters (temperature and concentration in the case of an

evaporation process, as in the work of Diefes (1997)). For instance, see the property

models proposed by Choi and Okos (1986);

ii) by assimilating the properties of individual pseudo-components to the properties of one or

more well-known chemical components considered as representative of the component

category: for instance, Byluppala (2010) modelled milk fat as mixture of 12 fatty acids,

3
 and Zhang et al. (2014) represented milk fat by a mixture of palmitic acid and oleic acid.

This approach can be criticized, because assimilating complex milk fat to one or several

specific acids is “unacceptable” from a physico-chemical point of view: Fat is present in

milk mainly as fat globules with a far more complex structure and composition than those

of individual fatty acids (see details in section 2.2.1 and Croguennec et al. (2008) for more

information on milk fat composition);

iii) by “artificially” developing the properties of individual pseudo-components in order to

match the desired mixture properties by simple addition of these individual properties

(Cheng & Friis, 2007). They may be developed through trial-and-error procedures, or

parameters optimisation. Such a decomposition has its limits, since all properties of food

product are not additive (see for instance viscosity), and therefore cannot be accurately

modelled by adding the individual properties of food components.

It is worth noting that the commercial software SuperPro Designer (Intelligen Inc.), which is a batch

process simulator designed for various biochemical and specialty industries (pharmaceutical,

microelectronics, wastewater, etc.), also handles some food processes, as shown in the work of Tomasula

et al. (2013): a fluid milk processing plant is simulated, however no documentation could be retrieved

about the definition and the modelling of milk in the software (Table 1)

The analysis of the literature clearly pointed out that none of the existing approaches satisfies the needs

for food concentration processes simulation. Some methods yield a need for the development of new unit

operation mathematical models, which may be time-consuming and specific to the conditions of the study

(equipment type, nature of the product, etc.). The other methods are based on the additivity of the

properties of food components, which can be a major drawback in the case of some properties.

In order to use the potential of chemical process software along with their unit operation models for food

applications, the objective of this work is to propose a new modelling strategy for food products. This

strategy is based on the incorporation, in commercial software, of the specific knowledge (from the

literature) of the properties of food product as a function of operating conditions (temperature,

concentration, composition). The approach consists in defining the food product as a mixture of water and

4
dry matter components (fat, proteins, carbohydrates, minerals, fibres in the general case) for which the

mixture properties are calculated with food property models selected from a literature analysis and

implemented as subroutines of the process software. This modelling method is derived from the second

group of approaches previously reviewed, with the significant difference that the mixture properties are

not simply an addition of the individual properties of the pseudo-components: the variations of the

mixture properties depending on temperature, pressure, concentration and composition are computed, the

composition being represented by the fraction of water and of the dry matter pseudo-components. In some

cases the model requires the individual properties of water, which are integrated in the thermodynamic

database of the flowsheeting software tool that will be adopted in this study (its choice will be justified).

The feasibility and benefits of the strategy proposed are investigated for the concentration of milk using

an evaporation step. Among other food sectors, the dairy sector largely uses concentration operations

such as vacuum evaporation. The evaporation step is considered, together with spray drying, as the most

energy intensive operation in the dairy industry: despite recent process improvements, the concentration

and drying steps still consume nowadays about 25% of the total energy used in dairy processing (French

Ministry of agriculture, food and forestry, 2011). In this work, industrial data taken from the work of

Ribeiro & Andrade (Ribeiro, 2001; Ribeiro & Andrade, 2003) and experimental data from experiments

performed with a pilot-scale evaporator used in the Dairy platform in Rennes (UMR STLO INRA-

Agrocampus Ouest, Rennes France) serve as a test bench to validate the modelling approach and illustrate

the potentialities of the proposed food modelling.

5
 Table 1 : Liquid food process models and simulations used in chemical process simulators

Origin of the data to

Food type &
Reference Food unit operations modelled Software (company) compare the simulation Limits to usability in this study
definition
with
Milk (non- Aspen Plus (AspenTech)
Unique component

Ribeiro, 2001; Ribeiro Preheating, pasteurization, Unit operation models include milk
conventional unique with Fortran 77 unit Industrial data
and Andrade, 2003 evaporation properties in their code
approach

component) operation models

Bon et al., 2010 Pasteurization Whole milk ProSimPlus (ProSim) Theoretical process No concentration involved
Aspen HYSYS Unit operation models include
Jorge et al., 2010 Evaporation Sugarcane juice Industrial data
(AspenTech) sugarcane properties in their code
Evaporation, spray drying, Milk : water, fat,
Matlab with Simulink
Diefes, 1997 ultrafiltration, heat exchanger, proteins, Theoretical processes Simulator developed internally
(MathWorks)
pumping, holding carbohydrates, ash
Heat transfer coefficient models
Orange juice : water, Experimental data from
Chawankul et al., 2001 Evaporation Aspen Plus (AspenTech) includes empirical property models ;
Pseudo-component approach

dry component laboratory and plant scales

undocumented modelling in streams
Miranda and Simpson, Tomato juice : water,
Evaporation Undocumented Industrial data Simulator developed internally
2005 dry component
Fat standardization, Milk : water, fat,
Cheng and Friis, 2007 homogenization, pasteurization, proteins, Pro/II (Invensys) Theoretical process No concentration involved
cooling carbohydrates, ash
Pasteurization, sterilization, Milk : water, fat, No concentration involved ;
Modelica with Dymola
Skoglund, 2007 homogenization, pumping, proteins, Industrial data simulator developed internally
(Dassault Systemes)
storage carbohydrates, ash (Commercial library of models)
No validation because no Modelling of chemical interactions
Milk : water, lactose,
Byluppala, 2010 Evaporation, settling, extraction Aspen Plus (AspenTech) experimental data was is required to simulate the extraction
12 fatty acids
available in the literature process
Undefined

Homogenization, storage,
approach

preheating, pasteurization, SuperPro Designer No concentration involved ;

Tomasula et al., 2013 Undocumented Theoretical process
holding, fat standardization, (Intelligen Inc.) undocumented milk properties
homogenization, cooling

6
2. Materials and methods

2.1. Modelling of milk

2.1.1. Assumptions on the “milk” system

In this study, bovine milk is considered as a mixture of water and four dry components: fat, proteins,

carbohydrates, and minerals. During a concentration step by evaporation, water is supposed to be the only

component that is removed. In reality, evaporated water drags away a small fraction of dry matter, thus

producing “cow waters” which are known to contain a small quantity of organic matter (100-150 mg of

Chemical Oxygen Demand per litre). In this work, the dragging of dry matter in evaporated water is

considered as negligible and not taken into account in calculations.

This study focuses on the physical properties of bovine milk varying with temperature, concentration and

composition. The properties of milk may also be affected by variations in the chemical structure of milk

components (mainly proteins), caused by heat treatment in milk powder production processes: protein

denaturation is known to occur during evaporation, but the changes affect only a small amount of the total

proteins compared to thermal treatments preceding evaporation (preheating, pasteurization), and occur in

even lesser proportions during drying (Oldfield, Taylor, & Singh, 2005; Singh & Creamer, 1991). Since

these changes are minor and poorly documented, they have not been taken into account in the present

work.

The previous assumptions (no dragging of dry matter constituents; no protein denaturation) imply that:

 There is no need to specify a chemical formula for dry components, since they all are considered

inert in a chemical sense;

 Vapour phase properties have to be specified a priori only for water (water properties are readily

available in most chemical process flowsheeting software), since dry matter components are

supposed not to be dragged in the vapour phase;

 The models of milk properties are only valid for the liquid phase (no milk component in the

vapour phase), and can include temperature and the mass fraction of any component of milk as

variables.

7
2.1.2. Molecular weight of milk pseudo-components

Most chemical process simulators require molecular weight as a fundamental property, and some property

models depend on the molecular weight of milk components (e.g. boiling point). Therefore, it is necessary

to allocate individual molecular weights to the dry matter components. The molecular weights of milk

components chosen in this study are a direct representation of the physico-chemical reality of the

components in milk.

Fat:

In milk, fat is mainly organized into spherical fat globules, with a diameter ranging from 0.1 to 15

µm (mean value around 4 µm). These globules have a core mostly made of triglycerides, and are

surrounded by a native biological membrane mainly composed of phospholipids (i.e. polar lipids)

and proteins. In order to be more representative of the natural organisation of fat in milk, it is

preferable to estimate the “bulk molecular weight” of a single fat globule, instead of retrieving the

molecular weight of the various components of milk fat and computing their weighted average.

Since milk is always homogenized before evaporation, homogenized milk is considered for the

estimation of the number of fat globules per unit volume as well as of the molecular weight of a

mean fat globule. Homogenization is performed up to 20 MPa results in about 16 fat globules per

µm3 (Walstra, Wouters, & Geurts, 2006). From the number of fat globules per volume unit, and

assuming a milk fat concentration of 36 g.L-1, the molecular weight of a fat globule is estimated to

be 1.35 × 109 g.mol-1. This value is representative of the physico-chemical characteristics of fat in

milk and is quite different from the value of Byluppala (2010), where milk fat is modelled as a

mixture of 12 fatty acids ranging from caproic acid (116.16 g.mol-1) to stearic acid (284.47 g.mol-1),

and from the work of Zhang et al. (2014) where milk fat is modelled as a mixture of palmitic and

oleic acids (256.42 g.mol-1 and 282.46 g.mol-1 respectively). Winchester (2000) specified a

molecular weight of 3 × 104 g.mol-1 for milk fat but no explanation was given regarding the choice

of this value.

Proteins:

Bovine milk proteins are classically divided into two major groups: i) whey proteins make up for

about 20% of the total protein content; they are also called soluble proteins, because they do not
8
 precipitate during cheese manufacture; ii) Caseins represent the remaining 80% of the total protein

content, and are aggregated into protein structures, called micelles; these micelles are responsible

for the white colour of milk due to light diffraction. In the calculation of the molecular weight of

proteins, only caseins micelles are considered in this work. Assuming an amount of 1018 micelles

per litre of milk (Fox & Brodkorb, 2008) and a casein concentration of 27 g.L-1, a casein micelle

weighs 2.7 × 10-17 g, which gives a “molecular weight” of about 1.63 × 107 g.mol-1 for a micelle.

This value is significantly different from the one used in Zhang et al. (2014) where the average

molecular weight of milk proteins, represented by casein, is set to 23000 g.mol-1. In the work of

Winchester (2000), the molecular weight of milk proteins is set to 24000 g.mol-1. The values used

by both Winchester (2000) and Zhang et al. (2014) have no physical meaning since caseins are

mainly not present under the form of individual molecules in milk but associated into micelles.

Carbohydrates:

Carbohydrates in milk consist mostly in lactose. Therefore the molecular weight of lactose was used,

i.e. 342 g.mol-1.

Minerals:

Milk also contains mineral substances which are partially dissolved in the aqueous phase of milk,

and partially complexed with themselves and/or with proteins. The molecular weight of milk

minerals was computed as the average molecular weight of the major mineral constituents of milk

in aqueous phase (milk saline constituents such as potassium, calcium, inorganic phosphate, soluble

citrate, etc.), weighted by their respective fractions as given in the work of Gaucheron (2005). The

obtained molecular weight for milk ash was 50 g.mol-1.

Molecular weight values used for this work are grouped in Table 2.

Table 2: Molecular weight values of milk dry matter components from different works
Milk dry matter component This study Winchester (2000) Zhang et al. (2014)
Fat 1,35E+09 30 000 269,4
Proteins 1,63E+07 24 000 23 000,0
Carbohydrates (lactose) 342,3 300 342,3
Minerals 50,1 100 66,5

2.1.3. Key properties of milk

Several physical properties of the food product require modelling, so that the behaviour of milk through
9
process steps can be mathematically described (Aspen Technology, 2011; Cheng & Friis, 2007; Ribeiro,

2001; Smith, 2011; Zhang et al., 2014):

 For mass and energy balances, the heat capacity and the boiling point are required. The heat

capacity is used to calculate enthalpy and energy balances, and the boiling point is involved in

vapour-liquid equilibrium (the so-called “flash calculations”). In the case of mixtures with water

as a solvent, the boiling point elevation (BPE) is used to express the temperature difference

between the boiling point of water and the one of the mixture at the same pressure.

 Simulations for unit operations design involve the evaluation of density, thermal conductivity,

viscosity, and surface tension.

The properties of milk are modelled mostly with empirical models (i.e. based on correlations obtained

from the fitting of experimental data) which were found in the literature.

2.2. Process flowsheeting simulation

2.2.1. Selection of a process flowsheeting simulator

The Aspen Plus simulator (Aspen Technology, Inc., Burlington, USA) was selected for this work. This

simulator has a strong capacity to integrate component models that are not included in its built-in

database, and allows an easy access to the property parameters of the components, as well as to the

models of the physico-chemical properties. A major advantage of this simulator is its interoperability,

which facilitates its coupling with optimisation procedures (You et al., 2012). This asset is particularly

attractive for further use of the simulator in eco-design approaches where the process performance is

accounted for.

2.2.2. Implementation of properties in the simulators

In Aspen Plus, as in most simulators, thermodynamic models must be selected to compute the physico-

chemical properties of individual components (or pseudo-components) and mixtures involved in the

process. Mixture property models generally involve “sub-models” for the individual properties of

chemical components (ideal gas heat capacity, vapour pressure, liquid density, etc.), which require

component-specific parameters and specific scalar parameters for chemical components (normal boiling
10
point, enthalpy of formation, etc.). These parameters were not used in this study, because they are not

known for three of the major components of milk dry matter (fat, proteins, minerals), and their complex

estimation is beyond the scope of this work (for instance, how to estimate a dipole moment value for milk

fat, or a value for the standard enthalpy of formation of milk caseins?).

Instead of adapting the food product model to existing property models, as it has been achieved in

previous works (Bon et al., 2010; Byluppala, 2010; Zhang et al., 2014), the available food product models

were, in this work, directly integrated in the simulator: the key mixture property models defined in Aspen

Plus were replaced by external Fortran programs (defined as “user models” in Aspen Plus), where each

milk property model selected from the literature was implemented. The Fortran programs are used by the

simulator when the corresponding liquid mixture property has to be computed. This concerns the molar

enthalpy (which contains the model for heat capacity), the activity coefficient (from which the BPE

stems), the molar volume (calculated from a mass density model), the thermal conductivity, the viscosity,

and the surface tension. In the case of the BPE, a subroutine was created to replace the activity coefficient

model, where the BPE is calculated and its value is added to the water saturation temperature value,

giving a “target” boiling point value that the activity coefficient has to match. The details of the

calculation can be found in Appendix A. With this method, any model for each key property of milk that

is required (i.e. heat capacity, boiling point elevation, density, thermal conductivity, viscosity, and surface

tension) can be written in a Fortran 77 program used by Aspen Plus. It must be highlighted that:

 the vapour mixture enthalpy model was defined as the ideal gas model, which is an acceptable

hypothesis since only water is supposed to evaporate (Sun & Hu, 2003);

 since the considered food product is in liquid state, and the evolution of thermodynamic state goes

from liquid to vapour through the water evaporation, the reference state for enthalpy calculations

was changed in Aspen Plus from ideal gas to liquid.

2.3. An industrial and a pilot-scale plants as references

In order to validate the models of the physico-chemical properties of milk, an industrial plant and a pilot

evaporation process were modelled in Aspen Plus.

11
2.3.1. Industrial milk concentration plant (Ribeiro, 2001; Ribeiro & Andrade, 2003)

The industrial milk concentration plant (Embaré Indùstrias Alimenticias S.A., Brazil) considered is the

one described by Ribeiro (2001) and Ribeiro & Andrade (2003). The milk process (Figure 1) consists of

two pre-heaters (HX-1, HX-2), a pasteurization unit (fed with hot water, Past-1), and a four-effect

evaporator (Evap-1 to 4). Each effect is made of a plate evaporator, followed by a centrifugal separator to

separate water vapour and milk concentrate. For each evaporator effect, 10% of the concentrate is

recycled to its feed. Steam enters the system at 6.67 bar and is sent to a thermocompressor (TP – 101)

before feeding the evaporators. The thermocompressor and the preheaters use recycled vapour from the

evaporator effects, which reduces the overall steam consumption. This process treats 11352 kg/h of a

standardised bovine whole milk (12% total solid), and produces 2742 kg/h of milk concentrate with a 48%

total solids content.

Figure 1: Flowsheet of the industrial evaporation plant used for the validation of the models of physic-

chemical models (Ribeiro, 2001)

It must be highlighted that the industrial process studied in Ribeiro (2001) should not be taken as a

standard scheme for the dairy industry. The process leads to the recycling of the concentrate, which is

prohibited today due to the risk of a too long product residence time, resulting in high protein denaturing

and bacterial growth in the concentrate (Fuquay, Fox, & McSweeney, 2011; Heldman & Lund, 2006).

Moreover the use of plate evaporators is less frequent compared to other evaporation technologies, such

as falling-film (tubular) evaporators (Decloux & Rémond, 2009).

12
2.3.2. Pilot-scale evaporator (Silveria et al., 2013)

A pilot-scale, single-effect falling-film evaporator (GEA Process Engineering, St Quentin-en-Yvelines)

available in Rennes (Dairy Platform, STLO, INRA) was used to validate the property models at

experimental scale. This equipment has already been described by Silveria et al. (2013). It is made of

three evaporation tubes connected to an indirect condenser integrated in the separator. Each tube is

arranged in its own body fed with fresh steam (saturated at 75°C) and undergoes the same vacuum

pressure (0.02 MPa). The flowsheet of the evaporator is shown in Figure 2. Two experiments involving

milk were performed at a feed flow rate of 50 kg/h, a first run with skim milk at 10% total solids

concentrated to 24%, and a second run with the concentrate at 24% up to 52% total solids (Silveira et al.,

2013).

Figure 2: Flowsheet of the pilot evaporator described in Silveira et al. (2013)

2.3.3. Modelling of industrial and experimental plants in Aspen Plus

The unit operations involved in both the industrial and the pilot-scale process were modelled using the

built-in blocks in Aspen Plus, listed in

Table 3. The pre-heaters and the pasteurizer of the industrial plant (Ribeiro, 2001; Ribeiro & Andrade,

2002) were modelled with “Heater” blocks, which perform heat and mass balances on a stream under

varying pressure or temperature, or exchanging heat. Due to the unusual geometry of the plate

13
evaporators involved in this industrial process (Ribeiro, 2001; Ribeiro & Andrade, 2002), it is not

possible to model this equipment in a detailed way with the Aspen Plus tools alone. A user model is

necessary to account for the geometry of the plates, following a similar approach to that adopted in

Ribeiro & Andrade (2002) where a rigorous mathematical model was developed. Instead, the evaporator

effects were modelled according to the same method as the pre-heaters and pasteurizer, in order to

perform heat and mass balances. A “Flash2” block was added to simulate the separation between liquid

and vapour streams. The obtained flowsheet is shown in Figure 3 and the operating conditions specified

in the different Aspen Plus blocks are given in Appendix C, Table B.3:.

Table 3: Aspen Plus blocks used to model the industrial process and the pilot evaporator
Unit operation Aspen Plus blocks with flowsheet reference code
Heater HX-1A for heat source (vapour condensation) and Heater HX-1A for heat
Pre-heaters 1 & 2
exchange with milk
Heater Pasto-1A for heat source (hot water temperature decrease) and Heater Pasto-
Pasteurizer
1A for heat exchange with milk
Stabilizing tank Heater STank (temperature decrease)
1 effect to compute heat and mass balances
= 1 Heater (Evap-iA; i being the effect n°) for steam/vapour condensation
4-effect evaporator (Evap-1 to Evap-4)
+ 1 Heater (Evap-iB) for heat exchange with milk
+ 1 Flash2 (Sep-i) for the separation of concentrate and evaporated water
1 tube to compute output from input and geometry
Mono-effect pilot evaporator, 3 tubes
= 1 Valve (Vac-A to Vac-C) to set inlet milk stream to vacuum pressure
+ 1 HeatX (F1-A to F1-C) to model the tube and surrounding shell
+ 1 Flash2 (Sep-A to Sep-C) for the separation of concentrate and evaporated water

Figure 3: Flowsheet of the evaporation process modelled in Aspen Plus to perform heat and mass

balances. The flowsheet is based on an industrial process previously described in the work of Ribeiro

(Ribeiro, 2001; Ribeiro & Andrade, 2003). For the legend, see

Table 3.

In the case of the pilot-scale process (Silveira et al., 2013), the evaporator was modelled on one hand with

Heater blocks to perform heat and mass balances, and on the other hand in a detailed way with the Aspen
14
Plus “HeatX” block. HeatX is a standard heat exchanger block which comprises the possibility to model

shell and tube heat exchangers, and the pilot falling film evaporator may be assimilated to a vertical,

downward flow shell and tube heat exchanger. Sufficient data is available in Silveira et al. (2013) on the

equipment design and geometry, and on the flow rates and operating conditions of the inlet streams. The

geometry of the evaporator tubes was specified in the HeatX block, with the parameters shown in

Appendix C, Table B.5:, along with the operating conditions specified in the different Aspen Plus blocks.

Because the HeatX block is designed to model industrial-size heat exchangers, modelling a pilot-size heat

exchanger requires a few tweaks in the HeatX block, which are documented in the Aspen support website

(http://support.aspentech.com/) and available from the corresponding author. The resulting flowsheet is

presented in Figure 4, and the flowsheet of the same process for heat and mass balanced only is presented

in Figure 5.

Figure 4: Flowsheet of the pilot evaporator (Silveira et al., 2013) modelled in Aspen Plus to predict

performance according to geometry of the equipment. For the legend, see

Table 3.

Figure 5: Flowsheet of the pilot evaporator (Silveira et al., 2013) modelled in Aspen Plus to predict

heat and mass balances. For the legend, see

Table 3.

2.4. Strategy for the identification and validation of milk property models
15
2.4.1. Identification of milk property models

Prior to the development of the Aspen Plus database, adequate models must be selected to compute the

properties of milk required for the simulation, i.e. heat capacity, BPE, density, thermal conductivity,

viscosity, and surface tension. A selection of models from the literature was carried out, so that only

models valid for bovine milk (or assumed bovine milk when not specified) and varying with at least

temperature and concentration were considered.

The different models describing the same property were compared to each other and to experimental data

within their validity ranges. For that purpose, each specific property was computed using the various

literature models at 3 or 4 different levels of dry matter, in a range of temperature compatible with

evaporation process. The dry matter levels correspond to the dry matters of milk, of a 50%-concentrated

milk and, of an intermediate milk concentrate. When experimental values were available, the property

was also computed at a fourth dry matter content, corresponding to the dry matter content of the

experimental values. The initial milk composition used to compute property values was not always the

same for the different properties, because property models were compared to experimental values, which

were retrieved from various works and obtained with various milk compositions.

For each property, the computed milk property values were plotted on 4 graphs, each corresponding to a

dry matter level. Only values with the range of validity of the model were displayed in the graphs. Error

bars represented the relative or absolute error between the model and the experimental values, when given

by the authors of the model.

2.4.2. Sensitivity analysis on the properties

Once the property models had been implemented in the simulator, a sensitivity analysis of the process

performance to the milk property models was performed with the pilot-scale plant in order to identify

which properties had the highest impact. With such information it is possible to define which property

models should be improved to reach a better accuracy in the predictions of the process model.

The pilot-scale process (Silveira et al., 2013) was chosen for the sensitivity study, because the geometry

of the equipment can be modelled in Aspen Plus (see Section 2.3.3). It must be highlighted that the

computation of vertical tubular heat exchanger models, which include equipment design and geometry, is

performed by default with the Steiner-Taborek correlation (Steiner & Taborek, 1992) implemented in the
16
HeatX model (Aspen Technology, 2011). However, this correlation is valid for a Reynolds number of at

least 4000, whereas preliminary simulation tests showed that in this study, the Reynolds number is never

higher than 700, and changes in viscosity modelling gave no change in simulation results (a 0.01%

difference in output dry matter percentage appeared for a reduction in viscosity computed values by at

least 1000). In order to study the sensitivity of the simulation to all six major properties of milk, the

Steiner-Taborek correlation was replaced with the correlation of Alhusseini et al. (1998). This correlation

has a wider range of validity (Reynolds number from 124 to 15600), and depends on the Reynolds,

Prandtl and Kapitza numbers, therefore its output is directly related to the value of heat capacity, density,

thermal conductivity, surface tension and viscosity of milk. With the additional information provided by

vapour-liquid equilibrium calculation affected by the BPE model, the influence of the six key properties

of milk on simulation results can be studied. For more details on the heat transfer coefficient subroutine

implemented in Aspen Plus, and the correlation of Alhusseini, see Appendix B.

With the use of such heat transfer coefficient model, it was possible to design a series of experiments with

6 properties (6 factors) and 2 levels for each factor, leading to a maximum of 64 experiments required.

The first level of each property/factor was the value calculated by the original property model (i.e.

without modification), and the second level was the value increased by 10%. The observed response was

the final product concentration obtained at the output of the last evaporator effect.

2.4.3. Validation of the property models integrated to a simulation tool

The validation of the implementation of selected property models in the simulator is useful to confirm

whether the chosen property models correctly reproduce the behaviour of milk undergoing evaporation

process. This validation was performed by comparison of industrial or pilot-scale data with the results of

the simulation for a given unit operation.

The heat capacity and BPE models were validated using heat and mass balances, which do not require

information on the equipment design and geometry. Only inlet and outlet streams conditions, flow rates

and heat exchanged between steam and milk in the evaporators are required. Validation could be

performed with both the systems (industrial and pilot scale plants – see section 2.3), since relevant data

were available. The other properties of milk (density, thermal conductivity, viscosity, surface tension)

required for design purposes were validated only with the information taken from the pilot scale
17
evaporator (Silveira et al., 2013).

3. Results

3.1. Choice of milk property models

The comparison of the different property models is described in this section, property by property.

3.1.1. Heat capacity

Two empirical models describe the liquid heat capacity of bovine milk as a function of temperature and

concentration: the model Fern nde -Mart n (1972a) and the one of Minim et al. (2002). The empirical

model of Choi & Okos (1986) was also selected because of its applicability to numerous liquid food

products. Figure 6 shows the variation of heat capacity with temperature for 4 different dry matters

(16.7%, 25.0%, 28.0%, 50.0%). At 28.0% dry matter content, milk composition matched the composition

of the whole milk with which the experimental data was measured (as mentioned in the legend of each

figure).

From the comparison of the three models for heat capacity (Figure 6), the model of Choi & Okos (1986)

was chosen because of a satisfying match with both empirical models of Fern nde -Mart n (1972a) and

Minim et al. (2002). Besides, a wider validity temperature and dry matter ranges than the other models

are proposed. At 16.7% dry matter, all models exhibited a close agreement. At 25.0% and 28.0%, the

relative difference with empirical models and experimental data was not higher than 6 %. The model of

Choi & Okos (1986) was the only one that could predict the heat capacity of milk concentrates at high dry

matter (> 28.0 %) and high temperature (> 75-80°C). However it must be highlighted that no

measurement of the heat capacity of whole milk concentrated at 50% could be found in the literature.

Another set of experimental data is required for a further validation of the model of Choi & Okos (1986)

at high concentrations (this aspect is beyond the scope of this work).

In the case of skim milk (0.44% fat content from the work of Minim et al. (2002)), the model of Choi &

Okos (1986) also fitted well the experimental data points, because of its wide validity ranges for

temperature and concentration, and it was supported by experimental data at low concentrations (see

Appendix D).

18
 (a) (b)

(c) (d)
Figure 6: Heat capacity of whole milk (83.3% water, 7.7% fat, 3.5% protein, 4.8% lactose, 0.7%
minerals) as a function of temperature for 4 different dry matter contents of milk concentrates ((a): 16.7%;
(b): 25.0%; (c): 28.0%; (d): 50.0%). Models are plotted only when they are in their range of validity. The
error bars on the data of Choi & Okos (1986) represent the standard error, given by the authors between
their model and experimental values obtained with an “evaporated milk” (no fat content given). In the
case of the Minim model, the error bars represent the mean relative difference, specifically calculated for
this study, from the model and the given experimental data.
3.1.2. Boiling Point Elevation (BPE)

To our knowledge, only one generic model for the prediction of boiling point elevation of milk

concentrates was reported in the literature. Assuming an ideal mixture between milk components,

Winchester (2000) calculated the BPE as a function of the heat of vaporization of water, the boiling

temperature of water, and the molar fraction of solute components. This model was only developed from

a theoretical basis, which no experimental data supported in the case of whole milk. Figure 7 shows the

BPE values calculated both for whole and skim milks (standard composition) at 60°C. In the case of

whole milk (Figure 7(a)), only the theoretical model of Winchester (2000) was studied, with no

19
experimental data to bring support. In the case of skim milk (Figure 7(b)), a satisfying agreement between

experimental and predicted values of the model was found. The model of Winchester (2000) was

therefore selected for this study, although the validation with experimental data for whole milk has not yet

been performed. The obtained BPE values were relatively low, (≤ 1°C in the case of whole milk).

However the BPE is not to be neglected, particularly in the case of mechanical compression of vapour in

evaporators (APV, 2006).

(a) (b)
Figure 7: Boiling point elevation of whole ((a): 87.1% water, 3.6% fat, 3.4% protein, 4.8% lactose, 1.1%
minerals) and skim ((b): 90.7% water, 0.3% fat, 3.5% protein, 4.8% lactose, 0.7% minerals) milk as a
function of dry matter. For whole milk (a) the curves overlap. For skim milk (b) experimental data was
given by an industrial partner (TGE - Thermique-Genie-Chimique-Evaporation, 300 rue Clément Ader,
27000 Evreux, France). MW = Molecular Weight.

Since the BPE model from Winchester (2000) depends on the molecular weight of the mixture

components through molar fractions (Table 4), its sensitivity to molecular weight was tested: the BPE

was computed with the molecular weight values used in the work of Winchester (2000), the ones

proposed in this work, and the ones from the work of Zhang et al. (2014) (see Table 2 and Figure 8). The

molecular weight values are given in Table 2, and the results in Figure 8. The influence of fat is clearly

visible: the highest difference between BPE values occur in the case of whole milk (Figure 8(a)): at 49%

dry content, the molecular weight values of Zhang et al. (2014) produce a BPE of 1.22°C and the values

of Winchester (2000) a BPE of 0.76°C. It can be concluded from these results that the choice of

molecular weight values seem to have a relatively small effect on the computation of the BPE. It should

be noted that with the values of Zhang et al. (2014) for the molecular weight, higher BPE values are

obtained for whole milk than for skim milk, which is inconsistent with current knowledge (water activity

in skim milk is lower - see Lewicki (2004) and other authors regarding water activity in milk and other
20
food products).

(a) (b)
Figure 8: Boiling point elevation of whole ((a): 87.1% water, 3.6% fat, 3.4% protein, 4.8% lactose, 1.1%
minerals) and skim ((b): 90.7% water, 0.3% fat, 3.5% protein, 4.8% lactose, 0.7% minerals) milk as a
function of dry matter. The model used to compute BPE is the same (Winchester, 2000). Only the
molecular weight values (MW) differ for each curve.
3.1.3. Density

Choi & Okos (1986), Fern nde -Mart n (1975), and Minim et al. (2002) developed models for the

prediction of milk density. In the case of Fern nde -Mart n (1975), two models are available: the former

predicts the thermal expansion coefficient (i.e. the change in volume in response to a change in

temperature) of milk, while the latter predicts the volume increase per unit mass of milk (respectively

indicated as “expansion coeff” and “vol increase” in Figure 9). The agreement between the model of Choi

& Okos (1986) and experimental data for the density of milk was satisfying, as shown in Figure 9 for

whole milk, and in Appendix D for skim milk respectively. There was a more significant discrepancy

between the models of Choi & Okos (1986) and of Fern nde -Mart n (1975), particularly in the case of

skim milk at intermediate dry matter (see Appendix D, Figure C.3:). Since the model of Choi & Okos

(1986) is supported by experimental data in a large range of dry matter content and is valid for a wider

range of temperature and dry matter content compared to the other existing models, the density model of

Choi & Okos (1986) was chosen for this study.

21
 (a) (b)

(c) (d)

Figure 9: Density of whole milk (83.3% water, 7.7% fat, 3.5% protein, 4.8% lactose, 0.7% minerals) and
concentrates for different dry matter contents ((a): 16.7%; (b): 25.0%; (c): 28.0%; (d): 50.0%). The error
bars on the data of Choi & Okos (1986) represent the standard error, given by the authors between their
model and experimental values obtained with an “evaporated milk” (no fat content given). In the case of
the Minim model, the error bars represent the mean relative difference, specifically calculated for this
study, from the model and the given experimental data.
3.1.4. Thermal conductivity

The model of Choi & Okos (1986) for thermal conductivity were compared with the models of Minim et

al. (2002), Fernández-Martín & Montes (1972), and Riedel (1949). Experimental data from the work of

Minim et al. (2002) supported the comparison at 28% dry matter. For skim milk, (see Appendix D), all

models were mutually consistent and also agree with experimental data. However in the case of whole

milk (Figure 10), although the models of Choi & Okos (1986), Minim et al. (2002), and Riedel (1949)

were in a relatively good agreement, the model of Fern nde -Mart n & Montes (1972) gave values that

are strongly different from the three others (33% difference between for Fernández-Martín & Montes
22
(1972) and Choi & Okos (1986) at 20°C and 16.7% dry matter content, Figure 10(a)). This sharp

discrepancy can be explained by the high fat-to-solids-non-fat ratio of milk, taken from Minim et al.

(2002) and considered as a reference. For the sake of comparison, the model developed by Fernández-

Martín & Montes (1972) was used with the same fat-to-solids-non-fat ratio, which is higher than the

maximum fat-to-solids-non-fat ratio with which the model of Fernández-Martín & Montes (1972) was

developed. Another significant difference occurred between the models of Choi & Okos (1986) and

Riedel (1949) at 50% dry matter (Riedel was 24% higher than Choi & Okos at 90°C, see Figure 10(d)),

with a trend reversal of the model of Choi & Okos (1986) starting around 50°C. Here the model of Choi

& Okos (1986) was affected by the high fat content values: in the model of Choi & Okos (1986), the

thermal conductivity of fat is related to temperature (1st order) with a negative coefficient, according to

the Equation 1.

λFat =1.8071 × 10-1 -2.7604 × 10-3 × T -1.7749 × 10-7 × T2 ( 1 )

The 1st order coefficient (-2.7604) has a higher absolute value than 1st order coefficients of the other

components (proteins, carbohydrates, minerals), and is negative, consequently giving the decrease in

thermal conductivity values that was observed (Figure 10(d)).

The models of Choi & Okos and Riedel stood out as the most relevant models, although there was a lack

of experimental data on whole milk at 50% dry matter to establish which the best option was. Since the

model of Riedel (1949) exhibited a closer match to the trend of experimental data at 28% dry matter

(Figure 10(c)), it was chosen for this study.

23
 (a) (b)

(c) (d)
Figure 10: Thermal conductivity of whole milk (83.3% water, 7.7% fat, 3.5% protein, 4.8% lactose, 0.7%
minerals) for different dry matter contents ((a): 16.7%; (b): 25.0%; (c): 28.0%; (d): 50.0%). The error
bars on the data of Choi & Okos (1986) represent the standard error, given by the authors between their
model and experimental values obtained with an “evaporated milk” (no fat content given). In the case of
the Minim et al. (2002) model, the error bars represent the mean relative difference, specifically
calculated for this study, from the model and the given experimental data. The error bars on the data of
Fernández-Martín & Montes (1972) represent the 3% maximal difference with experimental data of the
model, and the error bars on the data of Riedel (1949) represent the 1% prediction error of the model,
both calculated by the authors of the respective studies.
3.1.5. Viscosity

The models of Alcântara et al. (2012), Fern nde -Mart n (1972b), Morison et al. (2013), and Reddy &

Datta (1994) were used for the calculation of viscosity of milk and milk concentrates. The comparison

between these models should be considered carefully, because viscosity is a rheological property which,

when the fluid is non-Newtonian, depends on the shear rate applied to the fluid: the rheological behaviour

of milk has been reported by several authors as non-Newtonian above about 30-35% dry matter (for

instance Vélez-Ruiz & Barbosa-Cánovas, 1998). The measurement of viscosity may therefore be highly

dependent on operating conditions of the experiment, mainly shear rate, which is specified when available,

24
and temperature.

The difference between models was clearly significant at low temperatures for whole milk, as shown in

Figure 11. In the case of skim milk, the gap between the model of Fern nde -Mart n (1972b) and other

models was higher. Experimental data supported the model of Morison et al. (2013) strenuously for both

whole and skim milks. Because of the support by experimental data and its widest range of validity, the

model of Morison et al. (2013) was chosen. Also, the model seemed to take into account the non-

Newtonian behaviour of milk above 30% dry matter (Morison et al., 2013), since the component-specific

coefficients Ai (see Table 4) were obtained from experimental data at both low and high dry matter

contents. One drawback of the model is that it has been fitted to experimental data taken at a shear rate of

2000 s-1, whereas the shear rate in evaporators is lower (less than 1000 s-1 (Ang, 2011)); recent research at

the STLO (INRA, Rennes, France) suggests however that at 300 s-1, the shear rate reaches a plateau

above which viscosity values remain unchanged. Nevertheless, the model was considered satisfying

enough for a first attempt at modelling milk viscosity in evaporators and other unit operations in the milk

concentration process.

25
 (a) (b)

(c) (d)

Figure 11: Viscosity of whole milk (87.1% water, 3.4% fat, 3.1% protein, 5.6% lactose, 0.8% minerals)
for 4 different dry matters ((a): 12.9%; (b): 20.0%; (c): 40.0%; (d): 50.0%). The model of Morison (2013)
has a prediction error up to 21% represented by error bars, and the model of ern nde - art n (1972b)
fits experimental data within 5%, also represented by error bars.
3.1.6. Surface tension

Several authors developed various models for the prediction of surface tension of milk: Bertsch (1983)

developed 3 models, one specific of whole milk, the second specific of skim milk, and the third is a

general form adapted for both whole and skim milk; Watson (1958) developed models for raw whole, raw

skim, and homogenized whole milk. Ang (2011) developed a model for the prediction of the surface

tension of skim milk. In spite of the number of models developed, these models only take into account the

dependence with the temperature and none of them develop correlations with concentration. Experimental

data of surface tension of various milks with various fat contents were found in the work of Mukherjee et

al. (2005). In Paramalingam et al. (2000), surface tension values are given for whole milk at 3

26
temperatures with 3 to 6 dry matter values, from which a model, valid between 20°C and 65°C and for a

dry matter content between 5% and 40% was regressed by the authors (Equation 2).

σMilk, whole = 50.085 -0.179 × T+5.781 × 10-4 × T2

(2)
2 -4
+0.0439 × DM -0.00627 × DM -7.210 × 10 × DM × T

The models of Bertsch (1983 - whole milk model and general model), Paramalingam et al. (2000) and

Watson (1958 - raw and homogenized whole milk models) were compared for whole milk at three levels

of concentration, although only the regression from the data of Paramalingam et al. (2000) varied with

dry matter content (see Figure 12). Regardless of the model, the trend of the curves was similar, revealing

a decrease of the surface tension with the increase in temperature. However, the values were significantly

different between the considered models (for instance, a 19% discrepancy was observed when comparing

the general model of Bertsch (1983) with the model of Watson (1958) for whole milk at 20°C). Figure 12

(d) shows a comparison between the models at a constant temperature of 20°C and varying dry matter

content: the gap between the models of Bertsch (1983) and the regression from the data of Paramalingam

was significant, particularly at high dry matter, whereas the experimental data from Mukherjee et al.

(2005) was closely matched by the models of Bertsch (1983).

The general model of Bertsch (1983) was chosen, because it was supported by the experimental data of

Mukherjee et al. (2005) for whole milk, and was valid for both whole and skim milks, although the

comparison requires more experimental investigation, with a focus on the surface tension of milk with

varying dry matter.

27
 (a) (b)

(c) (d) 20°C, variable dry matter

Figure 12: Surface tension of whole milk (87.0% water, 3.7% fat, 3.7% protein, 5.3% lactose, 0.2%
minerals) according to temperature for 3 different dry matters ((a): 13.0%; (b): 25.0%; (c): 50.0%), and
according to dry content for temperature fixed at 20°C (d). The error bars on the data of Bertsch (1983)
represent the 9.6% mean relative error calculated by the author.
The models previously discussed and selected for each of the six properties are gathered in Table 4.

28
 Table 4: Selected property models for milk and food components

Property Model Reference

With :
Heat capacity Choi and Okos,
(Cp) 1986

Boiling Point
Winchester,
Elevation
2000
(ΔTBPE)

With :
Choi and Okos,
Density (ρ)
1986

Thermal
conductivity Riedel, 1949
(λ)

With: Morison et al.,

Viscosity (μ)
2013

Surface General model (whole milk & skim milk):

Bertsch, 1983
tension (σ)

3.2. Influence of property models on simulation

The results obtained from the sensitivity study in relation to the 6 major properties of milk (heat capacity,

BPE, density, thermal conductivity, viscosity and surface tension) are presented in Table 5. The analysis

of the response of the pilot process simulation to variation in property values showed that it was mainly

sensitive to thermal conductivity, followed by density and viscosity, while surface tension, heat capacity

and BPE had response coefficients 20% lower than that of thermal conductivity.

This sensitivity study showed how improvements should be conducted in the case of the simulation of

dairy evaporator systems with Aspen Plus and the modelling of milk used in this study: efforts should be

focused on the improvement of the modelling of thermal conductivity, density and viscosity of milk.

29
 Table 5: Results of the sensitivity analysis. The numerical values are the coefficients obtained after
modelling the response of the system (the pilot concentration process), i.e. the final product concentration,
as a function of the factors applied to the variables, i.e. the major properties of milk (see Section 2.4.2).
The interactions between variables (λ-ρ, σ-μ, Cp-μ- ρ, etc.) are not relevant in this analysis, because the
purpose is to identify the most impacting properties, and the main variables (i.e. the properties) were
sufficient to model the simulation response up to 3 digits.
Thermal conductivity λ 0.304
Density ρ 0.179
Viscosity μ -0.081
Surface tension σ -0.052
Heat capacity Cp 0.039
BPE -4.10-4
Constant 0.169

3.3. Validation of the modelling tool including selected property models

Once the property models had been selected (Table 4), and had been implemented in Aspen Plus

according to the method explained in Section 2.2.2, industrial data and experimental data described in

Section 2.3 served as a test bench to validate the modelling approach of the properties of milk within the

simulator.

3.3.1. Validation of heat and mass balances

Performing heat and mass balances in Aspen Plus only calls for heat capacity and BPE models of milk.

The industrial process described in the work of Ribeiro (Ribeiro, 2001; Ribeiro & Andrade, 2003) was

modelled and simulated in Aspen Plus where the milk property models had been implemented. In Table 6

are given the results for the concentration of milk leaving each evaporator effect and the temperature of

the obtained concentrate.

Table 6: Simulation and industrial results in the case of the computation of heat and mass balances with
the industrial process (Ribeiro, 2001).
Outlet concentration (% total solids) Concentrate temperature (°C)
Evaporator
Industrial Simulation Industrial Simulation
effects Difference Difference
results results results results
Evap-1 &
20,51% 20,44% < 1% 66.0 66.2 < 1%
Sep-1
Evap-2 &
25,20% 25,16% < 1% 61.0 61.3 < 1%
Sep-2
Evap-3 &
32,85% 33,06% + 1% 56.0 55.8 < 1%
Sep-3
Evap-4 &
48,00% 49,19% + 2% 46.0 45.1 - 2%
Sep-4

30
The highest difference between experimental and simulated concentration values was obtained at the

highest milk concentrations: differences in concentration and temperature results were both low

(maximum 2 points of difference). These results are promising, and showed that in this case the

simulation produced results consistent with reality. However, improvements are still needed in heat and

mass balances modelling, because a variation of 1% dry matter content in the concentrate leaving the

evaporator leads to substantial additional costs in the drying step following evaporation. In the case of the

pilot-scale evaporator (results in Table 7), differences were notably higher for the outlet concentration (up

to 25%).

Table 7: Simulation and experimental results in the case of the computation of heat and mass balances
with the pilot-scale evaporator (Silveira et al., 2013)
Outlet concentration (% total solids) Concentrate temperature
Concentration experiment Experiment Simulation Difference Experiment Simulation Difference

From 10% to 24% total solids 24% 29% + 20% 60.0°C 60.6°C + 1%
From 24% to 52% total solids 52% 65% + 25% 60.0°C 62.6°C + 4%

Several reasons may be attributed to the differences between the simulation and the

industrial/experimental results:

i) The accuracy of the modelling of the properties of milk itself may be significant. In the case of

empirical models, there may be a cumulative error in the modelling of the properties of milk (heat

capacity and BPE) that can result from the accuracy of the model regression, from the accuracy of

the experimental measurement, or from the conditions in which measurements were conducted,

which might not be valid in the case of the simulated concentration process.

ii) Some phenomena occurring in the process were not taken into account in the simulation, such as

flow rate fluctuations, heat losses during the evaporation process, or fouling of the evaporator

tubes. Indeed, the present simulation overestimated the performance of the processes, because it

did not take into account heat losses and fouling, which both decrease heat transfer, resulting in

lower concentration of the final product. In the case of the pilot evaporator in particular, it is

assumed that steam transfers all its heating power (8.4 kW per evaporator tube) to the product,

which is not the case in reality.

iii) The given measurements were assumed to be carried out under a “steady-state” regime, which

31
 may be practically difficult to reach.

3.3.2. Validation of the simulation including equipment geometry

The detailed simulation (i.e. including the size and geometry of the equipment) of the pilot-scale

evaporator (Silveira et al., 2013) was performed in Aspen Plus, so as to validate the modelling approach

with the set of the 6 key properties of milk (heat capacity, BPE, thermal conductivity, density, surface

tension, viscosity). The results are given in Table 8: temperatures are correctly simulated, whereas high

differences in outlet concentration can be observed between simulations and experiments.

Table 8: Simulation and experimental results in the case study of the computation of a detailed simulation
with the pilot evaporator (Silveira et al., 2013)
Outlet concentration (% total solids) Concentrate temperature
Concentration experiment Experiment Simulation Difference Experiment Simulation Difference

From 10% to 24% total solids 24% 29% + 20% 60.0°C 60.6°C + 1%
From 24% to 52% total solids 52% 48% - 9% 60.0°C 61.3°C + 2%

Such discrepancies may come from different origins:

- Some physical parameters have not been taken into account for simplification purposes, such as

heat losses and fouling. However in this case the outlet concentration should be overestimated in

both cases;

- The simulation uses six different property models, therefore cumulating the inaccuracies of each

of these models;

- The assumptions for modelling the pilot evaporator may also contain inaccuracies, such as the

heat transfer coefficient model, which was developed for the falling film evaporation of pure

component liquids (Alhusseini et al., 1998).

Apart from model accuracy, the slight overestimation of the boiling temperature may come from the

accuracy of measurement, since the physical variables in the evaporator may vary as slightly as the

difference observed between the simulation and experimental data.

4. Conclusion

In order to use the potential of chemical process software tools along with their unit operation models for

food applications, a new modelling strategy for liquid food products was proposed. The concentration

32
process of milk by evaporation was selected to illustrate the methodology since it was identified as one of

the most energy intensive operations in the dairy industry. Through the different steps to define and

develop models of a liquid food product, several needs in modelling food properties and food processes

were identified:

i) The food product (milk in this case study) was defined as a mixture of water and four dry matter

components (fat, proteins, carbohydrates, minerals) modelled as “pseudo-components” in a

conventional simulator which was adapted to take into account the behaviour of the liquid food

product considered.

ii) The significant properties of the food product/ milk (heat capacity, boiling point elevation, thermal

conductivity, density, viscosity, and surface tension) were modelled based on the empirical

knowledge (translated into mathematical models) of the variation of product properties as a

function of variable parameters of the considered unit operation. In this work, milk properties

(heat capacity, boiling point elevation, thermal conductivity, density, viscosity, surface tension)

were modelled as a function of temperature, dry matter content and composition. Obviously, this

strategy highlighted the necessity to acquire knowledge, in particular about the relationship

between the final properties of the product and the operational parameters of the process.

iii) A sensitivity analysis on the process of interest showed that in this case, thermal conductivity,

density and viscosity of milk should be the first targets for improvement from a modelling point of

view.

iv) The final validation of the modelling tool was performed at two levels: on one hand heat and mass

balances of the industrial concentration process gave results matching accurately with industrial

values (error ≤ 2%), thus validating heat capacity and BPE models. On the other hand a more

complex approach, which entailed the geometry of the equipment, gave satisfying results for the

temperature. However regarding the outlet concentration, a difference of up to 20% between

experiment and simulation pointed out the need to improve the heat transfer coefficient model,

which has a major impact on simulation results.

Although applied to this case study, this approach was intended to serve as generic. The ambition of this

work is to give some guidelines that could be followed for another food product. This strategy also led to

33
the development of a simulation tool dedicated to the modelling and simulation of milk heat treatment

and evaporation processes. The built-in unit operation models of the process simulator, or user-developed

unit operation models, can be used to simulate a variety of concentration process configurations. Thus,

new process designs or new process configurations and operating parameters can be studied, with

multiple potential purposes: cost reduction, reduction of the environmental impact by reduction of the

energy consumption, and other eco-design scenarios.

Acknowledgements
The authors wish to acknowledge with thanks the contribution of Pierre Schuck and Arlan Silveira from
the French National Institute for Agricultural Research (UMR 1253 STLO INRA-Agrocampus Ouest),
and Benoit Colin from the French company TGE S.A. (Thermique-Genie Chimique-Evaporation).

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40
Appendices
A. Calculation of the liquid activity coefficient of water with BPE
1. The boiling temperature (saturation temperature) of pure water is calculated from the pressure
with the Antoine equation:

(For water: A = 5.11564, B = 1687.537, C = -42.98).

2. The boiling temperature of water affected by the dissolved dry components of milk is calculated
from a BPE model retrieved from the literature (see Table 4), the BPE being a specific property of
milk:

3. The activity of water in the mixture is computed from the following theoretical model (Berry et al.,
(2000)):

Therefore:

with the molar latent heat of vaporization of water at the milk temperature.

4. Since the definition of water activity leads to (Smith, 2011): , the activity
coefficient of water is computed as : , being the molar fraction of water
in milk.

For dry matter components, γ =1 is assumed. It is noteworthy that this assumption is inaccurate in the
case of dissolved substances, i.e. minerals, lactose and proteins (Walstra et al., 2006). This remains to
be improved in further developments of this work, if a more accurate model is required.

B. Calculation of the overall heat transfer coefficient in the HeatX model of Aspen
Plus
Aspen Plus provides an estimation of outlet streams properties and performs iterations until satisfying
conditions are reached in outlet streams, therefore there is no need to implement an algorithm for
solving the heat transfer coefficient value.
1. Compute average properties of product inside the evaporator; example with heat capacity:
where is the heat capacity of the product side inlet
stream, and is the heat capacity of the outlet product stream at the temperature and
concentration estimated by Aspen Plus.
2. Compute wavy-laminar contribution according to Alhusseini et al. (1998):

3. Compute turbulent contribution according to Alhusseini et al. (1998):

With:

4. Total contribution of wavy-laminar term and turbulent term is:

5. Compute product side heat transfer coefficient:

41
 where , and are respectively the average thermal conductivity, viscosity and
density of the product. is the gravitational acceleration.
6. Compute average properties of steam inside the evaporator;
7. Compute steam side heat transfer coefficient (Earle & Earle, 1983):

Where , and are respectively the average thermal conductivity, viscosity and
density of the condensate film. is the average condensate enthalpy, is the
average temperature in the steam side of the evaporator, and is the average wall
temperature of the tube, approximated as the average temperature between the average steam
side temperature and the average product side temperature. L is the tube length.
8. Compute overall heat transfer coefficient:

Where ε is the tube thickness and λ is the tube material thermal conductivity.
C. Process and unit operation parameters in Aspen Plus
Table B.1: Characteristics of the industrial feed streams (milk and steam)
Composition (mass %) Flow rate Vapour Temperature
Water Fat Proteins Lactose Ash (kg/h) fraction (°C)
Whole milk feed 87.5% 3.8% 3.3% 4.7% 0.7% 11351.6 0 7
Steam to effect 1 100% 4579.2 1 80
Vapour to effect 2 100% 1201.1 1 65.5

Table B.2: Characteristics of the pilot evaporator feed streams (milk and steam)
Concentration Composition (mass %) Flow rate Vapour Temperature
experiment Water Fat Proteins Lactose Ash (kg/h) fraction (°C)
10 to 24% DM 90.4% 0.3% 3.4% 4.8% 1.1% 50 60
Skim milk feed
24 to 52% DM 76.0% 0.7% 8.6% 12.0% 2.6% 50 60
Steam 100% 13 1 75

42
 Table B.3: Unit operations parameters specified in Aspen Plus for heat and mass balances computation with the industrial process

Holding
Pre-heaters Pasteurizer Evaporator effects
tubes
HX-1 HX-2 Past-1 STank Evap-1 Sep-1 Evap-2 Sep-2 Evap-3 Sep-3 Evap-4 Sep-4
Outlet
temperature 45 65 88
Constraints (industrial data)

(°C)
Cold side
Temperature
-17
difference
Outlet pressure
101,325 101,325 101,325 0 26,14 0 20,87 0 16,11 0 9,32 0
(kPa)
Outlet
temperature 42 65,5 70 62 58,5 51
Hot side (°C)
Outlet pressure
101,325 47,36 25,6 20,89 16,18
(kPa)
Heat Duty (W) 0 0 0 0
Table B.4: Unit operations parameters specified in Aspen Plus for heat and mass balances computation with the pilot evaporator
Evaporator vessels
F1-A Sep-A F1-B Sep-B F1-C Sep-C
Cold side Outlet pressure (kPa) 20 20 20
Constraints

Temperature change 0 0 0
Hot side
Outlet vapor fraction 0 0 0
Heat duty (W) 0 0 0

43
Table B.5: Unit operations parameters specified in Aspen Plus for detailed simulation in the case study of the pilot evaporator
Vacuum valves Evaporator vessels Separators
Vac-A to Vac-C F1-A F1-B F1-C Sep-A to Sep-C
Outlet pressure (kPa) 20 20 20 20 20
Cold side
Film Coefficients Calculated from geometry
Constraints

Pressure drop Calculated from geometry

Hot side
Film Coefficients Calculated from geometry
Heat duty (W) 0
Hot fluid in Shell
Flow direction Counter-current
Evaporator (HeatX) specifications

U Methods Film coefficients

TEMA shell type (standard) E - One pass shell
Exchanger orientation Vertical
Direction of tube side flow Down
Inside shell diameter (mm) 121 80 80
Length (m) 4 4 4
Material TP-304 Stainless Steel
Tubes characteristics
Inner diameter (mm) 36 24 24
Tube thickness (mm) 1 1 1

44
D. Comparison of property models for skim milk

(a) (b)

(c) (d)
Figure C.1: Heat capacity of skim milk (90.7% water, 0.4% fat, 3.5% protein, 4.8% lactose, 0.7%
minerals) as a function of with temperature for 4 different dry matter contents ((a): 9.4%; (b): 25.0%; (c):
28.0%; (d): 50.0%).

(a) (b)

45
 (c)
Figure C.2: Density of skim milk (90.7% water, 0.4% fat, 3.5% protein, 4.8% lactose, 0.7% minerals) as a
function of temperature for 3 different dry matter contents ((a): 9.3%; (b): 25.0%; (c): 50.0%).

(a) (b)

(c) (d)
Figure C.3: Thermal conductivity of skim milk (90.7% water, 0.4% fat, 3.5% protein, 4.8% lactose, 0.7%
minerals) as a function of temperature for 4 different dry matter contents ((a): 9.4%; (b): 25.0%; (c):
28.0%; (d): 50.0%).

46
 (a) (b)

(c) (d)
Figure C.4: Viscosity of skim milk (90.5% water, 0.5% fat, 3.5% protein, 4.9% lactose, 0.7% minerals) as
a function of temperature for 4 different dry matter contents ((a): 9.5%; (b): 23.8%; (c): 37.6%; (d):
50.0%).

Figure C.5: Surface tension of skim milk (90.0% water, 0.5% fat, 3.9% protein, 5.5% lactose, 0.2%
minerals) as a function of temperature for 10% dry matter content.

47